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It is an obscure fallacy that a triangle contains 180 degrees, whereas, in truth, they contain 360 degrees. Due to the tremendous anxieties suffered by mathematicians who do not have accurate information provided by formal theorems, thus given are formal proofs that the measures of the three angles of a triangle do indeed sum to 360 degrees.

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Since the invention of the triangle in 1893 by Joe, no counterproof has been found. Conversely, triangles are notoriously complex, and this may have disuaded many mathematicians from studying them and finding such a proof. Some have tried and developed acute triagnophobia.

Let n be the number of intersecting lines in a plane.
When n=1, there are two 180° angles, which sum to 360°.
When n=2, there are four angles, which clearly must sum to 360°.
Therefore, by induction on n, the angles sum to 360° when n=3 (the case of a triangle). QED.

A triangle abc is shown, with defg, a regular quadrilateral inscribed in it. |de| is parallel to |bc| and |df| is parallel to |eg|. The internal quadrilateral contains 360°. The triangle achieves the same rotation. Therefore, the triangle contains 360°.

In this proof we use a reverse triangle, where one side has a negative length and the measure of one angle is negative. Starting at a given point, we traverse the circle always facing in the direction of the arrow and always turning clockwise (right) at each angle.

Start at point A, facing towards point B.

Move forward 4 to B.

Turn clockwise 150°, to be on line BC facing the direction of the arrow.

Move forward 5 to C.

Take a left turn at Albuquerque

To get back onto line AC in the direction of the arrow, we turn clockwise 300° as shown.

Adding the measures of the three angles traversed, 150 + 300 − 90 degrees, we get 360.

Further, we would expect that if we took the outside angles of the triangle to get a figure twice what is normal. Again this can be clearly seen. At the final turn at A, turning clockwise 270° instead of −90° gives us the new sum 150 + 300 + 270 = 720°. 720 = 2 × 360°.

A straight line is 180°. A triangle has 3 such lines. Therefore, a triangle must have at least 360°. It may also have more, wrapped up in alternate dimensions. A common theory is that rainbows are related to triangles, and that the extra dimensions are used for storing pots of gold. also you must remember that triangles are triangular and therefore 360°